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Line 1: − + − <br /><br />+ − '''Differential Geometry''' studies properties of smooth shapes called "differentiable manifolds" by analyzing their curvature properties.+ − <br /><br />+ − '''Algebraic Geometry''' studies properties of shapes defined by algebraic equations, by making use of the additional structures these objects inherit from their algebraic nature.+ − <br /><br />+ − '''Topology''', broadly speaking, studies properties of shapes invariant under continuous deformations. + + + + + + + + + + + + + + +
reinstating lost material and formatting from the rewrite, adding more content
Geometry is the branch of mathematics that deals with properties of shapes. Primarily, the subject may be divided into three branches:
'''Geometry''' is the branch of mathematics that deals with properties of [[shape]]s and spatial relationships. In its modern form, it is the pure mathematics of [[point]]s and [[line]]s and [[curve]]s and [[surface]]s. It is one of the two most basic branches of [[mathematics]], the other being [[algebra]], the study of relationships between [[number]]s. Primarily, the subject may be divided into six branches:
* [[Euclidean geometry]] studies geometry where the [[parallel postulate]] is valid.
* [[Non-Euclidean geometry]] studies geometry where the parallel postulate is false.
* [[Differential geometry]] studies properties of smooth shapes called differentiable [[manifolds]] by analyzing their [[curvature]] properties.
* [[Algebraic geometry]] studies properties of shapes defined by [[algebraic]] [[equation]]s, by making use of the additional structures these objects inherit from their algebraic nature.
* [[Topology]], broadly speaking, studies properties of shapes invariant under [[continuous function]]s.
* [[Riemannian geometry]], a geometry developed by [[Riemann]].
There are a few main types of spatial forms:
* [[Point]]s, an infinitely small dot.
* [[Line]]s, an infinitely long set of points expanding in two opposite directions.
* [[Plane]]s, an infinitely wide set of lines, stretching out in four directions.
* [[Space]], all of the 3-dimensional space that points, lines, and planes exist ons.
[[category:geometry]]
[[category:geometry]]